For light, GA aircraft, is there a "standard" turn, and what does that mean?

Question

I have seen instructional sites that seem to indicate a 15 degree bank is a standard turn. The Turn Coordinator has 15 and 30 degree marks on it. Is 15 degrees a standard turn and what does this mean? Is there a general way to figure out what the radius of such a turn is or how long it would take to fly a circle at 15 degrees bank? Without trying to do the math, it seems that airspeed together with bank angle would determine the turn rate.

Answer 1

The FAA Aeronautical Information Manual defines 'standard rate turn' as,

A turn of three degrees per second.

This results in the completion of a full circle in 2 minutes. Every airplane must be able to complete a standard rate turn in order to be certified. The standard rate of turn is used as the main reference for bank angle.

GA aircraft are expected to turn at the standard rate of turn during holding, intercepting, tracking, approaches, departures etc.

You're correct that the airspeed determines the turn rate. As the turn rate is standardized, the bank angle becomes dependent on the air speed. From FAA-H-8083-15A Instrument Flying Handbook,

True airspeed determines the angle of bank necessary to maintain a standard-rate turn. A rule of thumb to determine the approximate angle of bank required for a standard-rate turn is to divide your airspeed by 10 and add one-half the result. For example, at 60 knots, approximately 9° of bank is required (60 ÷ 10 = 6 + 3 = 9); at 80 knots, approximately 12° of bank is needed for a standard-rate turn.

Answer 2

The part of your question concerning the standard turn rate is already answered by aeroalias, so let me focus on the physics behind it:

In a turn the wing has to produce a centripetal force in addition to the lift $L$ needed to support the aircraft's weight $m\cdot g$, requiring a bank angle $\Phi$. The aircraft flying at a speed $v$ will experience a load factor $n_z$ exceeding unity: $$n_z = \frac{L}{m\cdot g} = \frac{1}{cos\Phi}$$ The turn radius $R$ is $$R = \frac{v^2}{g\cdot tan\Phi} = \frac{v^2}{g\cdot\sqrt{n_z^2-1}}$$ and the turn rate (expressed as angular velocity $\Omega$ in radians per second) of that turn is $$\Omega = \frac{v}{R} = \frac{g\cdot tan\Phi}{v} = \frac{g\cdot\sqrt{n_z^2-1}}{v}$$ Now you can find out which radius and turn rate are flown with $\Phi$ = 15° of bank in a coordinated turn.

Parameters for turns with 15° bank angle (own work). A turn rate of 3° per second can only be flown with 15° of bank at a speed of 50 m/s (97.2 kts). Flying slower will require less bank for the same turn rate or result in a higher turn rate for the same bank angle.